The opening point of the match saw an epic 51-shot rally eventually won by Evans as he secured an early break.
The Brit had to battle to avoid being broken back but he held out and was able to serve out to take the opening match.
The pair then had one break each in the second set as it went to a tie break where the first three points were all breaks.
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Australian teenager De Minaur, who is ranked 38 in the world, went into a 3-1 lead before Evans started to dig in.
He went to 6-5 and had match point only for De Minaur to save it, but Evans made no mistake at 7-6 as he took the tie break 8-6.
He will now face French Open champion Nadal who is also the defending champion and hasn’t played since he was knocked out of Wimbledon by Roger Federer in the semi-finals.
"It was so hot, I'm just happy to get through. I'm good physically so I never doubt myself but it is hard out here," Evans said after the match.
It will be the first time that Evans has ever faced the Spaniard.
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